Verified solution · Exam P
This Exam P sample reference tests Uniform Distribution. The no-deductible mean identifies the uniform support as [1,19]. A deductible of 4 leaves a positive excess over a 15-unit interval; integrating that excess against density 1/18 gives 225/36=6.25, so choice B is correct.
Independent solution
Setup
Use the no-deductible expected payment to recover the lower endpoint of the uniform loss distribution.
Model
The loss therefore has constant density 1/18 on [1,19], and the second policy pays only the positive excess above 4.
Compute
Integrate the payment over the part of the support above the deductible.
Answer
The expected payment under the deductible policy is 6.25.
Continue without hunting through PDFs
The searchable 3108-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A research vessel's repair-cost index X is uniformly distributed from 0 to 24. A reserve pays the amount of X above an unknown activation threshold d and pays zero otherwise. The expected reserve payment is 3. Determine d.
For a uniform index on [0,24], the expected positive excess over d is (24-d)²⁄⁴⁸. Equating this to 3 gives 24-d=12 and hence d=12, so choice C is correct.
Setup
Represent the reserve payment as the positive part above the unknown threshold.
Model
Integrate the excess payment using the constant uniform density.
Compute
Set the expected payment equal to its specified value and retain the threshold within the support.
Answer
The reserve activates at a cost index of 12.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 388 Exam P univariate random variables practice problems.
Drill the method: Exam P Uniform Distribution problems
Continue in syllabus order
The 3108-page Probability Proof Manual reorganizes 718 verified Exam P solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
ActuaryProof. “SOA Exam P Sample Question #597 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
